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The Nucleus Physics - The Nucleus

Jharkhand Board (JAC) - STD 12 Science - Physics (Jharkhand - English Medium). 91 questions in this chapter.

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The Nucleus question types

91 questions across 6 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.

91
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6
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5
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Sample Questions

The Nucleus questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

Q 1M.C.Q (1 Marks)1 Mark
Ten grams of $^{57}Co$ kept in an open container beta$-$decays with a half$-$life of $270$ days. The weight of the material inside the container after $540$ days will be very nearly:
  • ✓
    $10g$
  • B
    $5g$
  • C
    $2.5g$
  • D
    $1.25g$

Answer: A.

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Q 2M.C.Q (1 Marks)1 Mark
The decay constant of a radioactive sample is $\lambda.$ The half-life and the average$-$life of the sample are respectively:
  • A
    $\frac{1}{\lambda}$ and $\Big(\text{ln}\frac{2}{\lambda}\Big)$
     
  • ✓
    $\Big(\text{ln}\frac{2}{\lambda}\Big)$ and $\frac{1}{\lambda}$
     
  • C
    $\lambda(\text{ln}2)$ and $\frac{1}{\lambda}$
     
  • D
    $\frac{\lambda}{(\text{ln})2}$ and $\frac{1}{\lambda}$

Answer: B.

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Q 3M.C.Q (1 Marks)1 Mark
The mass of a neutral carbon atom in ground state is:
  • ✓
    Exact 12u
  • B
    Less than 12u
  • C
    More than 12u
  • D
    Depends on the form of carbon such as graphite or charcoal.

Answer: A.

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Q 4M.C.Q (1 Marks)1 Mark
Magnetic field does not cause deflection in:
  • A
    $\alpha-\text{rays}$
  • B
    $\beta^+-\text{rays}$
  • C
    $\beta^--\text{rays}$
  • ✓
    $\gamma-\text{rays}$

Answer: D.

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Q 5M.C.Q (1 Marks)1 Mark
As compared to ${ }^{12} \mathrm{C}$ and ${ }^{14} \mathrm{C}$ atom has:
  • A
    Two extra protons and two extra electrons.
  • B
    Two extra protons but no extra electron.
  • ✓
    Two extra neutrons and no extra electron.
  • D
    Two extra neutrons and two extra electrons.

Answer: C.

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Q 61 Marks Question1 Mark
${ }^{32} \mathrm{P}$ beta-decays to ${ }^{32} \mathrm{S}$. Find the sum of the energy of the antineutrino and the kinetic energy of the $\beta$-particle. Neglect the recoil of the daughter nucleus. Atomic mass of ${ }^{32} \mathrm{P}=31.974 \mathrm{u}$ and that of ${ }^{32} \mathrm{~S}=31.972 \mathrm{u}$.
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Q 71 Marks Question1 Mark
  1. a. Calculate the energy released if ${ }^{238} \mathrm{U}$ emits an $\alpha$-particle.
  2. Calculate the energy to be supplied to ${ }^{238} \mathrm{U}$ it two protons and two neutrons are to be emitted one by one. The atomic masses of ${ }^{238} \mathrm{U},{ }^{234} \mathrm{Th}$ and ${ }^4 \mathrm{He}$ are $238.0508 \mathrm{u}, 234.04363 \mathrm{u}$ and 4.00260 u respectively.
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Q 81 Marks Question1 Mark
Calculate the minimum energy needed to separate a neutron from a nucleus with Z protons and N neutrons it terms of the masses $\mathrm{M_{Z.N},M_{Z,N-1}}$ and the mass of the neutron.
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Q 91 Marks Question1 Mark
Show that the minimum energy needed to separate a proton from a nucleus with Z protons and N neutrons is:
$\Delta\text{E}=(\text{M}_{\text{Z}-1,\text{N}}+\text{M}_{\text{H}}-\text{M}_{\text{Z,N}})\text{c}^2$
where $M_{\text{Z,N}}=$ mass of an atom with Z protons and N neutrons in the nucleus and $M_H=$ mass of a hydrogen atom. This energy is known as proton-separation energy.
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Q 102 Marks Questions2 Marks
The decay constant of $\text{ }^{197}_{80}\text{Hg}$ (electron capture to $\text{ }^{197}_{79}\text{Au}$) is $1.8 \times 10^{-4} S^{-1}.$​​​​​​​
  1. What is the half-life?
  2. What is the average-life?
  3. How much time will it take to convert 25% of this isotope of mercury into gold?
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Q 112 Marks Questions2 Marks
When a boron nucleus $\big(\text{ }^{10}_5\text{B}\big)$ is bombarded by a neutron, an $\alpha$-particle is emitted. Which nucleus will be formed as a result?
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Q 132 Marks Questions2 Marks
Lithium (Z = 3) has two stable isotopes $^6Li$ and $^7Li.$ When neutrons are bombarded on lithium sample, electrons and $\alpha$-particles are ejected. Write down the nuclear process taking place.
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Q 142 Marks Questions2 Marks
Complete the following decay schemes.
  1. $\text{ }^{226}_{88}\text{Ra}\rightarrow\alpha+$
  2. $\text{ }^{19}_8\text{O}\rightarrow\text{ }^{19}_9\text{F}+$
  3. $\text{ }^{25}_{13}\text{Al}\rightarrow\text{ }^{25}_{12}\text{Mg}+$
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Q 153 Marks Question3 Marks
Calculate the energy released by 1g of natural uranium assuming 200MeV is released in each fission event and that the fissionable isotope $^{235}U$ has an abundance of 0.7% by weight in natural uranium.
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Q 163 Marks Question3 Marks
Consider the situation of the previous problem. Suppose the production of the radioactive isotope starts at t = 0. Find the number of active nuclei at time t.
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Q 173 Marks Question3 Marks
If three helium nuclei combine to form a carbon nucleus, energy is liberated. Why can't helium nuclei combine on their own and minimise the energy?
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Q 183 Marks Question3 Marks
A uranium reactor develops thermal energy at a rate of 300MW. Calculate the amount of $^{235}U$ being consumed every second. Average released per fission is 200MeV.
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Q 193 Marks Question3 Marks
The half-life of a radioisotope is 10h. Find the total number of disintegrations in the tenth hour measured from a time when the activity was 1Ci.
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Q 215 Marks Questions5 Marks
$4 \times 10^{23}$ tritium atoms are contained in a vessel. The half-life of decay tritium nuclei is 12.3y. Find:
  1. The activity of the sample.
  2. The number of decay in the next 10 hours.
  3. The number of decays in the next 6.15y.
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Q 225 Marks Questions5 Marks
$^{238}U$ decays to $^{206}Pb$ with a half-life of $4.47 \times 10^9y$. This happens in a number of steps. Can you justify a single half for this chain of processes? A sample of rock is found to contain 2.00mg of $^{238}U$ and 0.600mg of $^{206}Pb$. Assuming that all the lead has come from uranium, find the life of the rock.
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Q 235 Marks Questions5 Marks
Calculate the Q-values of the following fusion reactions:
  1. $\text{ }^2_1\text{H}+\text{ }^2_1\text{H}\rightarrow\text{ }^3_1\text{H}+\text{ }^1_1\text{H}$
  2. $\text{ }^2_1\text{H}+\text{ }^2_1\text{H}\rightarrow\text{ }^3_2\text{H}+\text{n}$
  3. $\text{ }^2_1\text{H}+\text{ }^3_1\text{H}\rightarrow\text{ }^4_1\text{H}+\text{n}$
Atomic masses are
$\text{m}\big(\text{ }^2_1\text{H}\big)=2.014102\text{u}$
$\text{m}\big(\text{ }^3_1\text{H}\big)=3·016049\text{u}$
$\text{m}\big(\text{ }^3_2\text{H}\big)=3.016029\text{u}$
$\text{m}\big(\text{ }^4_2\text{He}\big)=4·002603\text{u}$
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Q 245 Marks Questions5 Marks
A point source emitting alpha particles is placed at a distance of 1m from a counter which records any alpha particle falling on its $1cm^2$ window. If the source contains $6.0 \times 10^{16}$ active nuclei and the counter records a rate of 50000 counts/ second, find the decay constant. Assume that the source emits alpha particles uniformly in all directions and the alpha particles fall nearly normally on the window.
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Q 25Case study (4 Marks)4 Marks
The half-life of ${ }^{226} \mathrm{Ra}$ is 1602 y . Calculate the activity of 0.1 g of $\mathrm{RaCl}_2$ in which all the radium is in the form of ${ }^{226} \mathrm{Ra}$. Taken atomic weight of Ra to be $226 \mathrm{~g} / \mathrm{mol}^{-1}$ and that of Cl to be $35.5 \mathrm{~g} / \mathrm{mol}^{-1}$.
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Q 26Case study (4 Marks)4 Marks
A sample contains a mixture of $^{108}Ag$ and $^{110}Ag$ isotopes each having an activity of 8.0 \times 10^8 disintegration per second. $^{110}Ag$ is known to have larger half-life than $^{108}Ag.$ The activity A is measured as a function of time and the following data are obtained.
Time (s) Activity (A) $(10^8$ disinte- grations $s^{-1})$ Time (s) Activity (A) $(10^8$ disinte-grations $s^{-1})$
20 11.799 200 3.0828
40 9.1680 300 1.8899
60 7.4492 400 1.1671
80 6.2684 500 0.7212
100 5.4115    
  1. Plot ln $\Big(\frac{\text{A}}{\text{A}_0}\Big)$ versus time.
  2. See that for large values of time, the plot is nearly linear. Deduce the half-life of $^{110}Ag$ from this portion of the plot.
  3. Use the half-life of $^{110}Ag$ to calculate the activity corresponding to $^{108}Ag$ in the first 50s.
  4. Plot In $\Big(\frac{\text{A}}{\text{A}_0}\Big)$ versus time for $^{108}Ag$ for the first 50s.
  5. Find the half-life of $^{108}Ag.$
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